Application 1. For the function y= 3x^2/ x^2-4 the first and second derivatives are given. y'= -24x/ (x^2-4)^2 a) Determine any intercepts b) Determine equation of vertical asymptotes. For vertical asymptotes, investigate function values on either side of the asymptote. c) Determine the equation of the horizontal asymptote and End Behaviors d) Interval of Increase/decrease and any local maximum and minimum points. e) Determine the intervals for which the curve is concave up/concave down. f) State the coordinates of any points of inflection. 2. The temperature T, in ^oC, as a function of t hours is () = - t^4 +2t^3-4t^2+7where 0 12. a) When is the temperature decreasing? b) What is the lowest temperature reached over the first 4 hours? Thinking 1. Sketch the graph of a function () that satisfy the following properties: () < 0 for (, 1) (5, ) () > 0 for (1,3) (6, ) Lim3+ () = Lim () = 0 (1) = (5) = 0 2. Find the values of a and b if the function f(x)=x^3 + ax^2+ bx -10 and f(x) decreases to x = 6 and then increases, and f (1) = 29. Communication 1. Is the function f(x)=2/(x-3) increasing? Justify